Download e-book for iPad: A Primer for the Monte Carlo Method by Ilya M. Sobol

By Ilya M. Sobol

ISBN-10: 0849313856

ISBN-13: 9780849313851

The Monte Carlo technique is a numerical approach to fixing mathematical difficulties via random sampling. As a common numerical procedure, the strategy grew to become attainable in basic terms with the arrival of desktops, and its software maintains to extend with every one new machine iteration. A Primer for the Monte Carlo approach demonstrates how functional difficulties in technological know-how, undefined, and alternate could be solved utilizing this system. The e-book gains the most schemes of the Monte Carlo strategy and offers a number of examples of its software, together with queueing, caliber and reliability estimations, neutron delivery, astrophysics, and numerical research. the one prerequisite to utilizing the publication is an realizing of simple calculus.

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Extra resources for A Primer for the Monte Carlo Method

Sample text

We then add one to the counter of rejections and turn to the next request. Each time Tk+l is computed, we have to check the condition for termination of the experiment: Tk+l > 5"'. Once this condition is satisfied, the experiment comes to an end. The counters give us the number of satisfied requests psat and the number of rejected requests p r e j . This experiment must be repeated N times (each time with different values of Y). Then the results of all the trials are averaged: and where the values psat,j and p r e j , j are the values of p,,t and prej obtained in the jth trial.

TNshould not necessarily be identical and independent; essentially, all that is required is that individual variables & do not play too great a role in the sum. It is this theorem that explains why normal random variables are so often encountered in nature. Indeed, whenever we meet an aggregate effect of a large number of small random factors, the resulting random variable is normal. For example, the scattering of artillery shells is almost always normal, since it depends on weather conditions in all the various regions of the trajectory as well as on many other factors.

Generally, we must first ascertain the probabilistic laws governing the functioning of the various parts of the system. Then the Monte Carlo method permits the computation of the probabilistic laws of the entire system, however complex it may be. Such methods of calculations are extremely helpful in planning enterprises. Instead of an expensive (and sometimes impossible) real experiment, we can cany out experiments on a computer, trying out various versions of job organization and equipment usage.

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A Primer for the Monte Carlo Method by Ilya M. Sobol

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